Question

the figure is composed of a right rectangular prism and a right triangular prism.
what is the surface area, in square inches, of this figure?
enter answer square inches

Explanation:

Step1: Analyze the rectangular prism (yellow)

The yellow part is a right rectangular prism with length \( l = 8 \) in, width \( w = 8 \) in, height \( h = 5 \) in. But we need to consider the combined figure. Wait, actually, the total figure is composed of a rectangular prism (let's check dimensions) and a triangular prism. Wait, maybe better to calculate surface area by parts:

First, the rectangular prism (yellow and green? Wait, no. Let's list all faces:

- Front and back faces: The front face has a rectangle (yellow) of \( 8 \times 5 \) and a triangle? Wait, no, the figure is a combination. Wait, the blue part is a triangular prism (right triangular prism) with triangle base. Wait, maybe the correct approach is to calculate the surface area of the composite figure by adding the surface areas of the two prisms and subtracting the overlapping area (since they are joined together, the overlapping face is internal and not part of the surface area).

First, identify the two prisms:

1. Right rectangular prism (let's say the lower part, yellow) with dimensions: length \( l = 8 \) in, width \( w = 8 \) in, height \( h_1 = 5 \) in. Wait, no, the height from bottom to the green top is 5 in? Wait, the total height on the right is 8 in, and the yellow part is 5 in, so the blue part's height is \( 8 - 5 = 3 \) in? Wait, maybe I misread. Let's check the dimensions:

- The blue prism: triangular base? Wait, the top face of the blue prism is a rectangle with length 10 in and width 4 in? Wait, no, the figure is composed of a right rectangular prism (maybe the green and yellow) and a right triangular prism (blue). Wait, maybe the correct way is to calculate the surface area by considering all external faces.

Alternative approach:

The composite figure has the following faces:

- Bottom face: square? Wait, the base of the yellow part is 8 in by 8 in? Wait, the yellow part's front face is 8 in (width) by 5 in (height), and the depth is 8 in? Wait, maybe the yellow prism is 8x8x5 (length 8, width 8, height 5). Then the blue prism is a triangular prism with a triangular base. Wait, the triangular base: the triangle has a base of 8 in (since the yellow prism's top face is 8 in) and height? Wait, the blue prism's length is 10 in? Wait, the blue prism's top face is 10 in by 4 in? No, the blue prism's dimensions: the front face is a triangle? Wait, maybe the blue prism is a right triangular prism with a right triangle base, where one leg is 8 - 5 = 3 in (height) and the other leg is 8 in (base), and the length of the prism is 10 in? Wait, this is getting confusing. Maybe better to use the formula for composite surface area:

Surface area of composite figure = Surface area of rectangular prism + Surface area of triangular prism - 2 * area of overlapping face (since they are joined, the overlapping face is internal and counted twice, so subtract twice? Wait, no: when two solids are joined, the overlapping area is subtracted once from each, so total subtract 2 * overlapping area? Wait, no: surface area of A + surface area of B - 2 * area of the face where they are joined (because that face is inside both A and B, so we need to remove it from both).

First, let's define the two prisms:

Prism 1: Right rectangular prism (yellow and green) with dimensions: length \( l = 8 \) in, width \( w = 8 \) in, height \( h_1 = 5 \) in. Wait, no, the height of the rectangular prism (from bottom to green top) is 5 in, and the blue prism is on top. The blue prism is a right triangular prism with a triangular base (right triangle) where one leg is \( 8 - 5 = 3 \) in (vertical leg), the other leg is 8 in (horizontal leg), and the length of the prism (depth) is 10 in? Wait, the blue prism's top face is a rectangle with length 10 in and width 4 in? No, the given dimensions are 10 in (length of blue prism), 4 in (width?), 8 in (total height on right), 5 in (height of yellow prism), 8 in (depth? Wait, the yellow prism's depth is 8 in, as per the 8 in label on the right front.

Wait, maybe the yellow prism is 8 (length) x 8 (width) x 5 (height). Then the blue prism is a triangular prism with a right triangle base: legs 3 in (8 - 5) and 8 in (width), and length 10 in? No, the blue prism's length is 10 in, and the width is 4 in? Wait, the top face of the blue prism is 10 in by 4 in, as per the labels.

Wait, maybe I should look at the surface area components:

1. Bottom face: 8 in x 8 in = 64 in².

2. Four side faces of the yellow prism: two faces are 8 in (length) x 5 in (height) = 40 in² each, and two faces are 8 in (width) x 5 in (height) = 40 in² each? Wait, no, if the yellow prism is 8x8x5, then the lateral surface area (excluding top and bottom) is 2*(8*5 + 8*5) = 2*(40 + 40) = 160 in². Then the top face of the yellow prism is 8x8 = 64 in², but this is covered by the base of the blue prism, so we subtract that (since it's internal).

Now the blue prism: a right triangular prism. Let's find its dimensions. The triangular base: the triangle has a base of 8 in (same as the yellow prism's top face width) and height of 3 in (8 - 5 = 3 in, since the total height on the right is 8 in, and the yellow prism's height is 5 in). Wait, no, the right side of the blue prism is 8 in total? Wait, the label on the right is 8 in, which is the total height from bottom to top of the composite figure. So the yellow prism's height is 5 in, so the blue prism's height (vertical) is 8 - 5 = 3 in. The blue prism's length is 10 in, and the width (depth) is 4 in? Wait, the top face of the blue prism is 10 in (length) x 4 in (width), as per the labels.

The triangular base of the blue prism: the triangle has a base of 8 in (since the yellow prism's top face is 8 in) and height of 3 in (vertical), and the length of the prism is 10 in? No, the length of the blue prism is 10 in, and the width (depth) is 4 in. Wait, maybe the blue prism is a right triangular prism with a right triangle base where one leg is 8 in (horizontal) and the other leg is 3 in (vertical), and the length of the prism is 10 in, but the depth (width) is 4 in? This is confusing. Maybe an alternative approach:

Let's list all external faces:

- Bottom: 8x8 = 64.

- Front: The front face is composed of the yellow rectangle (8x5) and the blue triangle (base 8, height 3). Area of front face: 8*5 + (8*3)/2 = 40 + 12 = 52.

- Back: Same as front: 52.

- Left: The left face is a rectangle? Wait, the left face: the yellow part is 8 in (height) x 8 in (depth)? No, the depth is 8 in? Wait, the yellow prism's depth is 8 in (as per the 8 in label on the right front). So the left face of the yellow prism is 8 (depth) x 5 (height) = 40 in². Then the blue prism's left face: the blue prism's length is 10 in, and the height is 3 in, and depth is 4 in? No, maybe the left face of the blue prism is a rectangle with length 10 in and height 3 in? Wait, no, the left face of the composite figure: the yellow part's left face is 8 (depth) x 5 (height) = 40, and the blue part's left face is 10 (length) x 3 (height) = 30? No, this is not matching.

Wait, maybe the correct dimensions are:

- Yellow prism: length = 8 in, width = 8 in, height = 5 in.

- Blue prism: triangular base with legs 8 in (base) and 3 in (height, since 8 - 5 = 3), and length = 10 in. Wait, no, the blue prism's length is 10 in, and the width (depth) is 4 in? The label on the blue prism's top is 10 in (length) and 4 in (width). So the blue prism is a right triangular prism with a right triangle base (legs 8 in and 3 in) and length 10 in, but the width (depth) is 4 in? No, this is conflicting.

Alternative approach: Use the formula for surface area of composite solids.

Surface area of composite figure = Surface area of rectangular prism + Surface area of triangular prism - 2 * area of the overlapping face (since they are glued together, the overlapping face is internal and counted twice, so we subtract 2 times its area? Wait, no: when you join two solids, the overlapping area is subtracted once from each, so total subtract 2*area? Wait, no: surface area of A is SA_A, surface area of B is SA_B. When joined, the overlapping area is A_overlap, which is part of SA_A and part of SA_B. So the total surface area is SA_A + SA_B - 2*A_overlap (because we counted A_overlap twice, once in SA_A and once in SA_B, but it's internal, so we need to subtract 2*A_overlap).

First, find SA of rectangular prism (yellow):

SA_rectangular = 2*(lw + lh + wh) = 2*(8*8 + 8*5 + 8*5) = 2*(64 + 40 + 40) = 2*(144) = 288 in².

Now, SA of triangular prism (blue):

A triangular prism has two triangular bases and three rectangular lateral faces.

Triangular base: right triangle with legs 8 in (base) and 3 in (height, since 8 - 5 = 3). Area of one triangular base: (8*3)/2 = 12 in². So two triangular bases: 2*12 = 24 in².

Lateral faces of triangular prism:

- One face: length of prism (10 in) * base of triangle (8 in) = 80 in².

- One face: length of prism (10 in) * height of triangle (3 in) = 30 in².

- One face: length of prism (10 in) * hypotenuse of triangle. Wait, the hypotenuse of the right triangle: sqrt(8² + 3²) = sqrt(64 + 9) = sqrt(73) ≈ 8.544 in. But the label on the blue prism's top is 4 in, so maybe the hypotenuse is 4 in? No, that can't be. Wait, the label on the blue prism's top is 10 in (length) and 4 in (width). So the top face of the blue prism is a rectangle with 10 in and 4 in, so the lateral face of the triangular prism corresponding to the hypotenuse is 10 in * 4 in = 40 in². Ah! So the triangular prism's lateral faces are:

- One face: 10 in * 8 in = 80 in² (corresponding to the base of the triangle).

- One face: 10 in * 3 in = 30 in² (corresponding to the height of the triangle).

- One face: 10 in * 4 in = 40 in² (corresponding to the hypotenuse of the triangle).

So lateral surface area of triangular prism: 80 + 30 + 40 = 150 in².

Total surface area of triangular prism: 24 (triangular bases) + 150 (lateral) = 174 in².

Now, the overlapping face: the face where the two prisms are joined. The yellow prism's top face is 8 in * 8 in = 64 in². The blue prism's base face (the face glued to the yellow prism) is the area of the triangular base? No, wait, the blue prism is glued to the yellow prism's top face, but the blue prism's base is a triangle? No, that can't be. Wait, maybe the yellow prism's top face is 8 in * 4 in, and the blue prism's base is a triangle? No, the labels are:

- Yellow prism: 8 in (width), 8 in (depth), 5 in (height).

- Blue prism: 10 in (length), 4 in (width), 3 in (height, 8 - 5 = 3), and the triangular face is 8 in (base) and 3 in (height).

Wait, I think I made a mistake in the yellow prism's dimensions. Let's re-express:

The composite figure has:

- A right rectangular prism (let's call it Prism A) with length = 8 in, width = 4 in, height = 5 in.

- A right triangular prism (Prism B) with a right triangle base (legs 8 in and 3 in) and length = 10 in.

Wait, the label on the blue prism's top is 10 in (length) and 4 in (width), so Prism A (yellow) is 8 in (length) x 4 in (width) x 5 in (height), and Prism B (blue) is a triangular prism with base triangle (legs 8 in and 3 in) and length 10 in, and width 4 in? No, this is still confusing.

Wait, let's look at the given numbers: 10, 4, 8, 5, 8.

Let's calculate the surface area by adding all external faces:

1. Bottom face: 8 in x 8 in = 64.

2. Top face: The top face of the blue prism is a rectangle with 10 in x 4 in = 40.

3. Front face: The front face has a rectangle (8 in x 5 in) and a triangle (base 8 in, height 3 in). Area: 8*5 + (8*3)/2 = 40 + 12 = 52.

4. Back face: Same as front: 52.

5. Left face: The left face is a rectangle with 10 in (length) x 8 in (height)? No, the height is 8 in (total height). Wait, the total height is 8 in, so the left face: from bottom to top, height 8 in, length 10 in? No, the left face's area: 10 in (length) x 8 in (height) = 80? No, the left face has the yellow part (5 in height) and blue part (3 in height). So left face: 10 in (length) x 5 in (yellow height) + 10 in (length) x 3 in (blue height) = 50 + 30 = 80.

6. Right face: The right face is a rectangle with 8 in (depth) x 8 in (height)? No, the right face's area: 8 in (depth) x 8 in (height) = 64? Wait, the right face is 8 in (depth) x 8 in (height) = 64.

Wait, no, the right face: the yellow part is 8 in (depth) x 5 in (height) = 40, and the blue part is 10 in (length) x 3 in (height) = 30? No, this is not matching.

Wait, maybe the correct way is:

- The composite figure has:

- A rectangular prism with length 8, width 8, height 5.

- A triangular prism with a right triangle base (legs 8 and 3) and length 10.

Surface area of rectangular prism: 2*(8*8 + 8*5 + 8*5) = 2*(64 + 40 + 40) = 288.

Surface area of triangular prism: 2*( (8*3)/2 ) + (8 + 3 + sqrt(8² + 3²))*10. Wait, the lateral surface area of a triangular prism is perimeter of base * length. The base triangle has legs 8 and 3, so hypotenuse is sqrt(64 + 9) = sqrt(73) ≈ 8.544. Perimeter of base: 8 + 3 + 8.544 ≈ 19.544. Lateral surface area: 19.544*10 ≈ 195.44. Total surface area of triangular prism: 2*(12) + 195.44 ≈ 24 +

Answer:

Step1: Analyze the rectangular prism (yellow)

The yellow part is a right rectangular prism with length \( l = 8 \) in, width \( w = 8 \) in, height \( h = 5 \) in. But we need to consider the combined figure. Wait, actually, the total figure is composed of a rectangular prism (let's check dimensions) and a triangular prism. Wait, maybe better to calculate surface area by parts:

First, the rectangular prism (yellow and green? Wait, no. Let's list all faces:

• Front and back faces: The front face has a rectangle (yellow) of \( 8 \times 5 \) and a triangle? Wait, no, the figure is a combination. Wait, the blue part is a triangular prism (right triangular prism) with triangle base. Wait, maybe the correct approach is to calculate the surface area of the composite figure by adding the surface areas of the two prisms and subtracting the overlapping area (since they are joined together, the overlapping face is internal and not part of the surface area).

First, identify the two prisms:

1. Right rectangular prism (let's say the lower part, yellow) with dimensions: length \( l = 8 \) in, width \( w = 8 \) in, height \( h_1 = 5 \) in. Wait, no, the height from bottom to the green top is 5 in? Wait, the total height on the right is 8 in, and the yellow part is 5 in, so the blue part's height is \( 8 - 5 = 3 \) in? Wait, maybe I misread. Let's check the dimensions:

• The blue prism: triangular base? Wait, the top face of the blue prism is a rectangle with length 10 in and width 4 in? Wait, no, the figure is composed of a right rectangular prism (maybe the green and yellow) and a right triangular prism (blue). Wait, maybe the correct way is to calculate the surface area by considering all external faces.

Alternative approach:

The composite figure has the following faces:

• Bottom face: square? Wait, the base of the yellow part is 8 in by 8 in? Wait, the yellow part's front face is 8 in (width) by 5 in (height), and the depth is 8 in? Wait, maybe the yellow prism is 8x8x5 (length 8, width 8, height 5). Then the blue prism is a triangular prism with a triangular base. Wait, the triangular base: the triangle has a base of 8 in (since the yellow prism's top face is 8 in) and height? Wait, the blue prism's length is 10 in? Wait, the blue prism's top face is 10 in by 4 in? No, the blue prism's dimensions: the front face is a triangle? Wait, maybe the blue prism is a right triangular prism with a right triangle base, where one leg is 8 - 5 = 3 in (height) and the other leg is 8 in (base), and the length of the prism is 10 in? Wait, this is getting confusing. Maybe better to use the formula for composite surface area:

Surface area of composite figure = Surface area of rectangular prism + Surface area of triangular prism - 2 area of overlapping face (since they are joined, the overlapping face is internal and counted twice, so subtract twice? Wait, no: when two solids are joined, the overlapping area is subtracted once from each, so total subtract 2 overlapping area? Wait, no: surface area of A + surface area of B - 2 * area of the face where they are joined (because that face is inside both A and B, so we need to remove it from both).

First, let's define the two prisms:

Prism 1: Right rectangular prism (yellow and green) with dimensions: length \( l = 8 \) in, width \( w = 8 \) in, height \( h_1 = 5 \) in. Wait, no, the height of the rectangular prism (from bottom to green top) is 5 in, and the blue prism is on top. The blue prism is a right triangular prism with a triangular base (right triangle) where one leg is \( 8 - 5 = 3 \) in (vertical leg), the other leg is 8 in (horizontal leg), and the length of the prism (depth) is 10 in? Wait, the blue prism's top face is a rectangle with length 10 in and width 4 in? No, the given dimensions are 10 in (length of blue prism), 4 in (width?), 8 in (total height on right), 5 in (height of yellow prism), 8 in (depth? Wait, the yellow prism's depth is 8 in, as per the 8 in label on the right front.

Wait, maybe the yellow prism is 8 (length) x 8 (width) x 5 (height). Then the blue prism is a triangular prism with a right triangle base: legs 3 in (8 - 5) and 8 in (width), and length 10 in? No, the blue prism's length is 10 in, and the width is 4 in? Wait, the top face of the blue prism is 10 in by 4 in, as per the labels.

Wait, maybe I should look at the surface area components:

1. Bottom face: 8 in x 8 in = 64 in².

1. Four side faces of the yellow prism: two faces are 8 in (length) x 5 in (height) = 40 in² each, and two faces are 8 in (width) x 5 in (height) = 40 in² each? Wait, no, if the yellow prism is 8x8x5, then the lateral surface area (excluding top and bottom) is 2(85 + 85) = 2(40 + 40) = 160 in². Then the top face of the yellow prism is 8x8 = 64 in², but this is covered by the base of the blue prism, so we subtract that (since it's internal).

Now the blue prism: a right triangular prism. Let's find its dimensions. The triangular base: the triangle has a base of 8 in (same as the yellow prism's top face width) and height of 3 in (8 - 5 = 3 in, since the total height on the right is 8 in, and the yellow prism's height is 5 in). Wait, no, the right side of the blue prism is 8 in total? Wait, the label on the right is 8 in, which is the total height from bottom to top of the composite figure. So the yellow prism's height is 5 in, so the blue prism's height (vertical) is 8 - 5 = 3 in. The blue prism's length is 10 in, and the width (depth) is 4 in? Wait, the top face of the blue prism is 10 in (length) x 4 in (width), as per the labels.

The triangular base of the blue prism: the triangle has a base of 8 in (since the yellow prism's top face is 8 in) and height of 3 in (vertical), and the length of the prism is 10 in? No, the length of the blue prism is 10 in, and the width (depth) is 4 in. Wait, maybe the blue prism is a right triangular prism with a right triangle base where one leg is 8 in (horizontal) and the other leg is 3 in (vertical), and the length of the prism is 10 in, but the depth (width) is 4 in? This is confusing. Maybe an alternative approach:

Let's list all external faces:

• Bottom: 8x8 = 64.

• Front: The front face is composed of the yellow rectangle (8x5) and the blue triangle (base 8, height 3). Area of front face: 85 + (83)/2 = 40 + 12 = 52.

• Back: Same as front: 52.

• Left: The left face is a rectangle? Wait, the left face: the yellow part is 8 in (height) x 8 in (depth)? No, the depth is 8 in? Wait, the yellow prism's depth is 8 in (as per the 8 in label on the right front). So the left face of the yellow prism is 8 (depth) x 5 (height) = 40 in². Then the blue prism's left face: the blue prism's length is 10 in, and the height is 3 in, and depth is 4 in? No, maybe the left face of the blue prism is a rectangle with length 10 in and height 3 in? Wait, no, the left face of the composite figure: the yellow part's left face is 8 (depth) x 5 (height) = 40, and the blue part's left face is 10 (length) x 3 (height) = 30? No, this is not matching.

Wait, maybe the correct dimensions are:

• Yellow prism: length = 8 in, width = 8 in, height = 5 in.

• Blue prism: triangular base with legs 8 in (base) and 3 in (height, since 8 - 5 = 3), and length = 10 in. Wait, no, the blue prism's length is 10 in, and the width (depth) is 4 in? The label on the blue prism's top is 10 in (length) and 4 in (width). So the blue prism is a right triangular prism with a right triangle base (legs 8 in and 3 in) and length 10 in, but the width (depth) is 4 in? No, this is conflicting.

Alternative approach: Use the formula for surface area of composite solids.

Surface area of composite figure = Surface area of rectangular prism + Surface area of triangular prism - 2 area of the overlapping face (since they are glued together, the overlapping face is internal and counted twice, so we subtract 2 times its area? Wait, no: when you join two solids, the overlapping area is subtracted once from each, so total subtract 2area? Wait, no: surface area of A is SA_A, surface area of B is SA_B. When joined, the overlapping area is A_overlap, which is part of SA_A and part of SA_B. So the total surface area is SA_A + SA_B - 2A_overlap (because we counted A_overlap twice, once in SA_A and once in SA_B, but it's internal, so we need to subtract 2A_overlap).

First, find SA of rectangular prism (yellow):

SA_rectangular = 2(lw + lh + wh) = 2(88 + 85 + 85) = 2(64 + 40 + 40) = 2*(144) = 288 in².

Now, SA of triangular prism (blue):

A triangular prism has two triangular bases and three rectangular lateral faces.

Triangular base: right triangle with legs 8 in (base) and 3 in (height, since 8 - 5 = 3). Area of one triangular base: (83)/2 = 12 in². So two triangular bases: 212 = 24 in².

Lateral faces of triangular prism:

• One face: length of prism (10 in) * base of triangle (8 in) = 80 in².

• One face: length of prism (10 in) * height of triangle (3 in) = 30 in².

• One face: length of prism (10 in) hypotenuse of triangle. Wait, the hypotenuse of the right triangle: sqrt(8² + 3²) = sqrt(64 + 9) = sqrt(73) ≈ 8.544 in. But the label on the blue prism's top is 4 in, so maybe the hypotenuse is 4 in? No, that can't be. Wait, the label on the blue prism's top is 10 in (length) and 4 in (width). So the top face of the blue prism is a rectangle with 10 in and 4 in, so the lateral face of the triangular prism corresponding to the hypotenuse is 10 in 4 in = 40 in². Ah! So the triangular prism's lateral faces are:

• One face: 10 in * 8 in = 80 in² (corresponding to the base of the triangle).

• One face: 10 in * 3 in = 30 in² (corresponding to the height of the triangle).

• One face: 10 in * 4 in = 40 in² (corresponding to the hypotenuse of the triangle).

So lateral surface area of triangular prism: 80 + 30 + 40 = 150 in².

Total surface area of triangular prism: 24 (triangular bases) + 150 (lateral) = 174 in².

Now, the overlapping face: the face where the two prisms are joined. The yellow prism's top face is 8 in 8 in = 64 in². The blue prism's base face (the face glued to the yellow prism) is the area of the triangular base? No, wait, the blue prism is glued to the yellow prism's top face, but the blue prism's base is a triangle? No, that can't be. Wait, maybe the yellow prism's top face is 8 in 4 in, and the blue prism's base is a triangle? No, the labels are:

• Yellow prism: 8 in (width), 8 in (depth), 5 in (height).

• Blue prism: 10 in (length), 4 in (width), 3 in (height, 8 - 5 = 3), and the triangular face is 8 in (base) and 3 in (height).

Wait, I think I made a mistake in the yellow prism's dimensions. Let's re-express:

The composite figure has:

• A right rectangular prism (let's call it Prism A) with length = 8 in, width = 4 in, height = 5 in.

• A right triangular prism (Prism B) with a right triangle base (legs 8 in and 3 in) and length = 10 in.

Wait, the label on the blue prism's top is 10 in (length) and 4 in (width), so Prism A (yellow) is 8 in (length) x 4 in (width) x 5 in (height), and Prism B (blue) is a triangular prism with base triangle (legs 8 in and 3 in) and length 10 in, and width 4 in? No, this is still confusing.

Wait, let's look at the given numbers: 10, 4, 8, 5, 8.

Let's calculate the surface area by adding all external faces:

1. Bottom face: 8 in x 8 in = 64.

1. Top face: The top face of the blue prism is a rectangle with 10 in x 4 in = 40.

1. Front face: The front face has a rectangle (8 in x 5 in) and a triangle (base 8 in, height 3 in). Area: 85 + (83)/2 = 40 + 12 = 52.

1. Back face: Same as front: 52.

1. Left face: The left face is a rectangle with 10 in (length) x 8 in (height)? No, the height is 8 in (total height). Wait, the total height is 8 in, so the left face: from bottom to top, height 8 in, length 10 in? No, the left face's area: 10 in (length) x 8 in (height) = 80? No, the left face has the yellow part (5 in height) and blue part (3 in height). So left face: 10 in (length) x 5 in (yellow height) + 10 in (length) x 3 in (blue height) = 50 + 30 = 80.

1. Right face: The right face is a rectangle with 8 in (depth) x 8 in (height)? No, the right face's area: 8 in (depth) x 8 in (height) = 64? Wait, the right face is 8 in (depth) x 8 in (height) = 64.

Wait, no, the right face: the yellow part is 8 in (depth) x 5 in (height) = 40, and the blue part is 10 in (length) x 3 in (height) = 30? No, this is not matching.

Wait, maybe the correct way is:

• The composite figure has:

• A rectangular prism with length 8, width 8, height 5.

• A triangular prism with a right triangle base (legs 8 and 3) and length 10.

Surface area of rectangular prism: 2(88 + 85 + 85) = 2*(64 + 40 + 40) = 288.

Surface area of triangular prism: 2( (83)/2 ) + (8 + 3 + sqrt(8² + 3²))10. Wait, the lateral surface area of a triangular prism is perimeter of base length. The base triangle has legs 8 and 3, so hypotenuse is sqrt(64 + 9) = sqrt(73) ≈ 8.544. Perimeter of base: 8 + 3 + 8.544 ≈ 19.544. Lateral surface area: 19.54410 ≈ 195.44. Total surface area of triangular prism: 2(12) + 195.44 ≈ 24 +